**(5x+11)/(x**

^{2}-9)**(4x-2)/(x**

^{2}-9)How would you solve this f(x)⁄g(x) problem (please include ALL steps and an explanation for each)?

f(x)=**(5x+11)/(x**^{2}-9)

g(x)= **(4x-2)/(x**^{2}-9)

Also, would the domain end up being (-∞, -3) U (-3, 1/2) U (1/2, 3) U (3, ∞)? Or would there be no 1/2? From what I think I got, the denominator should be 2(2x-1), so the denominator couldn't be 0, so it can't be 1/2. Am I right? Or would we just be looking in the middle of the solving/simplifying?

One last thing: when do we look in problems like these to get our domain (like when do we look to see what values are not included)?

Thanks!

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Marked as Best Answer

If you have variable in denominator, we

So, the first step will be to find the domain of f(x) and g(x),

x

Thus, both functions are defined for

x ∈ ( - ∞, - 3) U (- 3, 3) U (3, ∞)

........

After you finish division, you will insert another critical point x = 1/2 into domain of original functions.

Hi M;

I APOLOGIZE. I FORGOT ABOUT THE SECOND HALF OF THE EQUATION. HERE IT IS...

f(x)/g(x)=f(x) times 1/g(x)

(5x+11) (x^{2}-9)

(x^{2}-9) (4x-2)

I took g(x) and flipped the numerator and denominator to make this a multiplication rather than division question.

In this equation (x^{2}-9) is in both the numerator and denominator. These therefore cancel.

(5x+11)

(4x-2)

THE ONLY THING LIMITING THE CURRENT DOMAIN IS THAT X CANNOT = 1/2 TO RENDER THE NUMERATOR ZERO.

PLEASE ASK YOUR INSTRUCTOR IF WE SIMPLIFY AND THEN EVALUATE DOMAIN, OR IF WE EVALUATE DOMAIN BEFORE SIMPLIFICATION. I HAVE RESEARCHED THIS AND CANNOT FIND AN ANSWER.

Yes, this matches up with what I got! Thanks! I'll make sure to ask while reviewing for our test.

Please tell me the answer the instructor provides because I also need to know.

Okay, I will respond as soon as I find out!

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